This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses exponents and roots. By the end of the module students should be able to understand and be able to read exponential notation, understand the concept of root and be able to read root notation, and use a calculator having the
yx key to determine a root.

Section overview

Exponential Notation

Reading Exponential Notation

Roots

Reading Root Notation

Calculators

Exponential notation

Exponential notation

We have noted that multiplication is a description of repeated addition.
Exponen­tial notation is a description of repeated multiplication.

Suppose we have the repeated multiplication

8⋅8⋅8⋅8⋅8size 12{8 cdot 8 cdot 8 cdot 8 cdot 8} {}

Exponent

The factor 8 is repeated 5 times. Exponential notation uses a
superscript for the number of times the factor is repeated. The superscript is placed on the repeated factor,
85 , in this case. The superscript is called an
exponent .

The function of an exponent

An
exponent records the number of identical factors that are repeated in a multiplication.

Sample set a

Write the following multiplication using exponents.

3⋅3size 12{3 cdot 3} {} . Since the factor 3 appears 2 times, we record this as

Reading exponential notation

Base

Exponent, power

5 is called the
exponent , or
power .
85size 12{8 rSup { size 8{5} } } {} is read as "eight to the fifth power," or more simply as "eight to the fifth," or "the fifth power of eight."

Squared

When a whole number is raised to the second power, it is said to be
squared . The number
52size 12{5 rSup { size 8{2} } } {} can be read as

5 to the second power, or
5 to the second, or
5 squared.

Cubed

When a whole number is raised to the third power, it is said to be
cubed . The number
53size 12{5 rSup { size 8{3} } } {} can be read as

5 to the third power, or
5 to the third, or
5 cubed.

When a whole number is raised to the power of 4 or higher, we simply say that that number is raised to that particular power. The number
58size 12{5 rSup { size 8{8} } } {} can be read as

5 to the eighth power, or just
5 to the eighth.

Roots

In the English language, the word "root" can mean a source of something. In mathematical terms, the word "root" is used to indicate that one number is the source of another number through repeated multiplication.

Square root

We know that
49=72size 12{"49"=7 rSup { size 8{2} } } {} , that is,
49=7⋅7size 12{"49"=7 cdot 7} {} . Through repeated multiplication, 7 is the source of 49. Thus, 7 is a root of 49. Since two 7's must be multiplied together to produce 49, the 7 is called the second or
square root of 49.

Cube root

We know that
8=23size 12{8=2 rSup { size 8{3} } } {} , that is,
8=2⋅2⋅2size 12{8=2 cdot 2 cdot 2} {} . Through repeated multiplication, 2 is the source of 8. Thus, 2 is a root of 8. Since three 2's must be multiplied together to produce 8, 2 is called the third or
cube root of 8.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?

fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.

Tarell

what is the actual application of fullerenes nowadays?

Damian

That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.

Tarell

Join the discussion...

what is the Synthesis, properties,and applications of carbon nano chemistry

Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.